Moment Inequalities for Semiparametric Multinomial Choice with Fixed Effects∗

We propose a new approach to identification of multinomial choice models with a group (or panel) structure. The utility for each choice is additively separable in a choice-specific fixed effect, a disturbance, and an index function of covariates and parameters. Observations in the same group are assumed to share the same fixed effects. Special cases of our semiparametric model include Chamberlain’s (1980) conditional logit model for panel data problems with choice-specific fixed effects and models of product demand where markets are the grouping device, the within group observations are consumers, and the choice-specific fixed effects represent product level unobservables. We place no restriction on the variance-covariance of the disturbance vector across choices. The only restriction on the disturbances is a group homogeneity assumption. The main cost of the semiparametric flexibility is that the derived conditional moment inequalities only partially identify the index function parameters. The advantages of our framework are that (i) it is nonparametric in the joint distribution of